Construction of simplicial complexes with prescribed degree-size sequences.

We study the realizability of simplicial complexes with a given pair of integer sequences, representing the node degree distribution and the facet size distribution, respectively. While the s-uniform variant of the problem is NP-complete when s≥3, we identify two populations of input sequences, most of which can be solved in polynomial time using a recursive algorithm that we contribute. Combining with a sampler for the simplicial configuration model [J.-G. Young et al., Phys. Rev. E 96, 032312 (2017)2470-004510.1103/PhysRevE.96.032312], we facilitate the efficient sampling of simplicial ensembles from arbitrary degree and size distributions. We find that, contrary to expectations based on dyadic networks, increasing the nodes' degrees reduces the number of loops in simplicial complexes. Our work unveils a fundamental constraint on the degree-size sequences and sheds light on further analyses of higher-order phenomena based on local structures.

Community detection in bipartite networks with stochastic block models.

In bipartite networks, community structures are restricted to being disassortative, in that nodes of one type are grouped according to common patterns of connection with nodes of the other type. This makes the stochastic block model (SBM), a highly flexible generative model for networks with block structure, an intuitive choice for bipartite community detection. However, typical formulations of the SBM do not make use of the special structure of bipartite networks. Here we introduce a Bayesian nonparametric formulation of the SBM and a corresponding algorithm to efficiently find communities in bipartite networks which parsimoniously chooses the number of communities. The biSBM improves community detection results over general SBMs when data are noisy, improves the model resolution limit by a factor of sqrt[2], and expands our understanding of the complicated optimization landscape associated with community detection tasks. A direct comparison of certain terms of the prior distributions in the biSBM and a related high-resolution hierarchical SBM also reveals a counterintuitive regime of community detection problems, populated by smaller and sparser networks, where nonhierarchical models outperform their more flexible counterpart.

Nanoscopic substructures of raft-mimetic liquid-ordered membrane domains revealed by high-speed single-particle tracking.

Lipid rafts are membrane nanodomains that facilitate important cell functions. Despite recent advances in identifying the biological significance of rafts, nature and regulation mechanism of rafts are largely unknown due to the difficulty of resolving dynamic molecular interaction of rafts at the nanoscale. Here, we investigate organization and single-molecule dynamics of rafts by monitoring lateral diffusion of single molecules in raft-containing reconstituted membranes supported on mica substrates. Using high-speed interferometric scattering (iSCAT) optical microscopy and small gold nanoparticles as labels, motion of single lipids is recorded via single-particle tracking (SPT) with nanometer spatial precision and microsecond temporal resolution. Processes of single molecules partitioning into and escaping from the raft-mimetic liquid-ordered (Lo) domains are directly visualized in a continuous manner with unprecedented clarity. Importantly, we observe subdiffusion of saturated lipids in the Lo domain in microsecond timescale, indicating the nanoscopic heterogeneous molecular arrangement of the Lo domain. Further analysis of the diffusion trajectory shows the presence of nano-subdomains of the Lo phase, as small as 10 nm, which transiently trap the lipids. Our results provide the first experimental evidence of non-uniform molecular organization of the Lo phase, giving a new view of how rafts recruit and confine molecules in cell membranes.

A Rhizavidin Monomer with Nearly Multimeric Avidin-Like Binding Stability Against Biotin Conjugates.

Developing a monomeric form of an avidin-like protein with highly stable biotin binding properties has been a major challenge in biotin-avidin linking technology. Here we report a monomeric avidin-like protein-enhanced monoavidin-with off-rates almost comparable to those of multimeric avidin proteins against various biotin conjugates. Enhanced monoavidin (eMA) was developed from naturally dimeric rhizavidin by optimally maintaining protein rigidity during monomerization and additionally shielding the bound biotin by diverse engineering of the surface residues. eMA allowed the monovalent and nonperturbing labeling of head-group-biotinylated lipids in bilayer membranes. In addition, we fabricated an unprecedented 24-meric avidin probe by fusing eMA to a multimeric cage protein. The 24-meric avidin and eMA were utilized to demonstrate how artificial clustering of cell-surface proteins greatly enhances the internalization rates of assembled proteins on live cells.